Blair, Matthew Strichartz estimates for wave equations with coefficients of Sobolev regularity. (English) Zbl 1098.35036 Commun. Partial Differ. Equations 31, No. 4-6, 649-688 (2006). There is a contribution in the frame of general investigations regarding Strichartz type estimates for wave equations with nonsmooth coefficients. The strategy is to obtain estimates on components of the solution whose Fourier transform is highly localized. The coefficients of the wave operator should lie in a Sobolev space of sufficiently high order. Using the “wave packets technology” i.e. frame of \(L^2\) functions suited for analysis of wave operators one constructs a parametrix for the wave operator that is suitable for proving estimates. In the last two sections of the paper estimates via parametrix and via truncation/rescaling are shown. Reviewer: Claudia Simionescu-Badea (Wien) Cited in 4 Documents MSC: 35B45 A priori estimates in context of PDEs 35L05 Wave equation 35B65 Smoothness and regularity of solutions to PDEs 35R05 PDEs with low regular coefficients and/or low regular data Keywords:Strichartz estimates; wave equation; wave packets; dispersive estimates PDFBibTeX XMLCite \textit{M. Blair}, Commun. Partial Differ. Equations 31, No. 4--6, 649--688 (2006; Zbl 1098.35036) Full Text: DOI References: [1] DOI: 10.1155/S107379289900063X · Zbl 0938.35106 · doi:10.1155/S107379289900063X [2] DOI: 10.1353/ajm.1999.0038 · Zbl 0952.35073 · doi:10.1353/ajm.1999.0038 [3] DOI: 10.1006/jfan.1995.1119 · Zbl 0849.35064 · doi:10.1006/jfan.1995.1119 [4] DOI: 10.1007/BF01671936 · Zbl 0759.35014 · doi:10.1007/BF01671936 [5] DOI: 10.1353/ajm.1998.0039 · Zbl 0922.35028 · doi:10.1353/ajm.1998.0039 [6] DOI: 10.1006/jfan.1995.1075 · Zbl 0846.35085 · doi:10.1006/jfan.1995.1075 [7] Mockenhaupt G., J. Amer. Math. Soc. 6 pp 65– (1993) [8] Smith H., Ann. Inst. Fourier 48 pp 797– (1998) · Zbl 0974.35068 · doi:10.5802/aif.1640 [9] Smith H., Math. Res. Lett. 1 pp 729– (1994) · Zbl 0832.35018 · doi:10.4310/MRL.1994.v1.n6.a9 [10] Stein E. M., Singular Integrals and Differentiability Properties of Functions (1970) · Zbl 0207.13501 [11] Stein E. M., Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals (1993) · Zbl 0821.42001 [12] DOI: 10.1016/0022-1236(70)90027-3 · Zbl 0189.40701 · doi:10.1016/0022-1236(70)90027-3 [13] DOI: 10.1215/S0012-7094-77-04430-1 · Zbl 0372.35001 · doi:10.1215/S0012-7094-77-04430-1 [14] DOI: 10.1353/ajm.2000.0042 · doi:10.1353/ajm.2000.0042 [15] DOI: 10.1353/ajm.2001.0021 · Zbl 0988.35037 · doi:10.1353/ajm.2001.0021 [16] DOI: 10.1090/S0894-0347-01-00375-7 · Zbl 0990.35027 · doi:10.1090/S0894-0347-01-00375-7 [17] Taylor M. E., Pseudodifferential Operators and Nonlinear PDE (1991) · doi:10.1007/978-1-4612-0431-2 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.